Analysis of the trend to equilibrium of a chemically reacting system

In this present paper, a quaternary gaseous reactive mixture, for which the chemical reaction is close to its final stage and the elastic and reactive frequencies are comparable, is modelled within the Boltzmann equation extended to reacting gases. The main objective is a detailed analysis of the non-equilibrium effects arising in the reactive system A1 + A2 A3 + A4, in a flow regime which is considered not far away from thermal, mechanical and chemical equilibrium. A first-order perturbation solution technique is applied to the macroscopic field equations for the spatially homogeneous gas system, and the trend to equilibrium is studied in detail. Adopting elastic hardspheres and reactive line-of-centres cross sections and an appropriate choice of the input distribution functions—which allows us to distinguish the two cases where the constituents are either at same or different temperatures—explicit computations of the linearized production terms for mass, momentum and total energy are performed for each gas species. The departures from the equilibrium states of densities, temperatures and diffusion fluxes are characterized by small perturbations of their corresponding equilibrium values. For the hydrogen–chlorine system, the perturbations are plotted as functions of time for both cases where the species are either at the same or different temperatures. Moreover, the trend to equilibrium of the reaction rates is represented for the forward and backward reaction H2 + Cl HCl + H